German Patent No. DE 102 19 826 A1, for example, describes a method and a device for the field-oriented regulation of a synchronous machine. In this instance, the output variables of a direct-axis current regulator and of a cross current regulator are converted in a stationary decoupling network to a direct-axis component of voltage and a cross voltage component, and these are subsequently submitted to a limitation as a function of the rotational speed of the synchronous machine. The limited direct-axis components of voltage and the cross voltage components are transformed in a transformer into voltages of a polyphase three-phase current system. These voltages are passed on to a pulse-width-modulated inverter and converted by the latter to a control voltage for the synchronous machine. The polyphase machines mentioned are used, for instance, in electrical drives, especially for hybrid and electric vehicles. For the operation of the polyphase machine, pulse-width-modulated inverters are used. The electrical drives named have a series of diagnostic functions. With the use of these, one is usually able to determine complete failure of elements in the polyphase machine, particularly in the pulse-width-modulated inverter. These diagnostic functions, up to now, have been implemented in a comparatively effortful, and thus cost-laden manner.